PHYSICAL REVIEW D 052003 (2013) Measurement of the D ......25Indian Institute of Technology...

Measurement of theD�ð2010Þþ natural linewidth and the D�ð2010Þþ�D0 mass differenceJ. P. Lees,1 V. Poireau,1 V. Tisserand,1 E. Grauges,2 A. Palano,3a,3b G. Eigen,4 B. Stugu,4 D.N. Brown,5 L. T. Kerth,5

Yu. G. Kolomensky,5 G. Lynch,5 H. Koch,6 T. Schroeder,6 C. Hearty,7 T. S. Mattison,7 J. A. McKenna,7 R. Y. So,7

A. Khan,8 V. E. Blinov,9 A. R. Buzykaev,9 V. P. Druzhinin,9 V. B. Golubev,9 E. A. Kravchenko,9 A. P. Onuchin,9

S. I. Serednyakov,9 Yu. I. Skovpen,9 E. P. Solodov,9 K. Yu. Todyshev,9 A.N. Yushkov,9 D. Kirkby,10 A. J. Lankford,10

M. Mandelkern,10 B. Dey,11 J.W. Gary,11 O. Long,11 G.M. Vitug,11 C. Campagnari,12 M. Franco Sevilla,12 T.M. Hong,12

D. Kovalskyi,12 J. D. Richman,12 C. A. West,12 A.M. Eisner,13 W. S. Lockman,13 A. J. Martinez,13 B. A. Schumm,13

A. Seiden,13 D. S. Chao,14 C.H. Cheng,14 B. Echenard,14 K. T. Flood,14 D. G. Hitlin,14 P. Ongmongkolkul,14

F. C. Porter,14 R. Andreassen,15 C. Fabby,15 Z. Huard,15 B. T. Meadows,15 M.D. Sokoloff,15 L. Sun,15 P. C. Bloom,16

W. T. Ford,16 A. Gaz,16 U. Nauenberg,16 J. G. Smith,16 S. R. Wagner,16 R. Ayad,17,† W.H. Toki,17 B. Spaan,18

K. R. Schubert,19 R. Schwierz,19 D. Bernard,20 M. Verderi,20 S. Playfer,21 D. Bettoni,22a C. Bozzi,22a R. Calabrese,22a,22b

G. Cibinetto,22a,22b E. Fioravanti,22a,22b I. Garzia,22a,22b E. Luppi,22a,22b L. Piemontese,22a V. Santoro,22a

R. Baldini-Ferroli,23 A. Calcaterra,23 R. de Sangro,23 G. Finocchiaro,23 P. Patteri,23 I.M. Peruzzi,23,‡ M. Piccolo,23

M. Rama,23 A. Zallo,23 R. Contri,24a,24b E. Guido,24a,24b M. Lo Vetere,24a,24b M. R. Monge,24a,24b S. Passaggio,24a

C. Patrignani,24a,24b E. Robutti,24a B. Bhuyan,25 V. Prasad,25 M. Morii,26 A. Adametz,27 U. Uwer,27 H.M. Lacker,28

P. D. Dauncey,29 U. Mallik,30 C. Chen,31 J. Cochran,31 W. T. Meyer,31 S. Prell,31 A. E. Rubin,31 A.V. Gritsan,32

N. Arnaud,33 M. Davier,33 D. Derkach,33 G. Grosdidier,33 F. Le Diberder,33 A.M. Lutz,33 B. Malaescu,33 P. Roudeau,33

A. Stocchi,33 G. Wormser,33 D. J. Lange,34 D.M. Wright,34 J. P. Coleman,35 J. R. Fry,35 E. Gabathuler,35

D. E. Hutchcroft,35 D. J. Payne,35 C. Touramanis,35 A. J. Bevan,36 F. Di Lodovico,36 R. Sacco,36 M. Sigamani,36

G. Cowan,37 J. Bougher,38 D.N. Brown,38 C. L. Davis,38 A. G. Denig,39 M. Fritsch,39 W. Gradl,39 K. Griessinger,39

A. Hafner,39 E. Prencipe,39 R. J. Barlow,40,§ G. D. Lafferty,40 E. Behn,41 R. Cenci,41 B. Hamilton,41 A. Jawahery,41

D. A. Roberts,41 R. Cowan,42 D. Dujmic,42 G. Sciolla,42 R. Cheaib,43 P.M. Patel,43,* S. H. Robertson,43 P. Biassoni,44a,44b

N. Neri,44a F. Palombo,44a,44b L. Cremaldi,45 R. Godang,45,∥ P. Sonnek,45 D. J. Summers,45 X. Nguyen,46 M. Simard,46

P. Taras,46 G. De Nardo,47a,47b D. Monorchio,47a,47b G. Onorato,47a,47b C. Sciacca,47a,47b M. Martinelli,48 G. Raven,48

C. P. Jessop,49 J.M. LoSecco,49 K. Honscheid,50 R. Kass,50 J. Brau,51 R. Frey,51 N. B. Sinev,51 D. Strom,51 E. Torrence,51

E. Feltresi,52a,52b N. Gagliardi,52a,52b M. Margoni,52a,52b M. Morandin,52a M. Posocco,52a M. Rotondo,52a G. Simi,52a

F. Simonetto,52a,52b R. Stroili,52a,52b S. Akar,53 E. Ben-Haim,53 M. Bomben,53 G. R. Bonneaud,53 H. Briand,53

G. Calderini,53 J. Chauveau,53 Ph. Leruste,53 G. Marchiori,53 J. Ocariz,53 S. Sitt,53 M. Biasini,54a,54b E. Manoni,54a,54b

S. Pacetti,54a,54b A. Rossi,54a,54b C. Angelini,55a,55b G. Batignani,55a,55b S. Bettarini,55a,55b M. Carpinelli,55a,55b,¶

G. Casarosa,55a,55b A. Cervelli,55a,55b F. Forti,55a,55b M.A. Giorgi,55a,55b A. Lusiani,55a,55c B. Oberhof,55a,55b

E. Paoloni,55a,55b A. Perez,55a G. Rizzo,55a,55b J. J. Walsh,55a D. Lopes Pegna,56 J. Olsen,56 A. J. S. Smith,56

F. Anulli,57a R. Faccini,57a,57b F. Ferrarotto,57a F. Ferroni,57a,57b M. Gaspero,57a,57b L. Li Gioi,57a G. Piredda,57a

C. Bünger,58 O. Grünberg,58 T. Hartmann,58 T. Leddig,58 C. Voß,58 R. Waldi,58 T. Adye,59 E. O. Olaiya,59

F. F. Wilson,59 S. Emery,60 G. Hamel de Monchenault,60 G. Vasseur,60 Ch. Yèche,60 D. Aston,61 D. J. Bard,61

J. F. Benitez,61 C. Cartaro,61 M. R. Convery,61 J. Dorfan,61 G. P. Dubois-Felsmann,61 W. Dunwoodie,61 M. Ebert,61

R. C. Field,61 B.G. Fulsom,61 A.M. Gabareen,61 M. T. Graham,61 C. Hast,61 W.R. Innes,61 P. Kim,61 M. L. Kocian,61

D.W.G. S. Leith,61 P. Lewis,61 D. Lindemann,61 B. Lindquist,61 S. Luitz,61 V. Luth,61 H. L. Lynch,61

D. B. MacFarlane,61 D. R. Muller,61 H. Neal,61 S. Nelson,61 M. Perl,61 T. Pulliam,61 B.N. Ratcliff,61

A. Roodman,61 A.A. Salnikov,61 R.H. Schindler,61 A. Snyder,61 D. Su,61 M.K. Sullivan,61 J. Va’vra,61 A. P. Wagner,61

W. F. Wang,61 W. J. Wisniewski,61 M. Wittgen,61 D.H. Wright,61 H.W. Wulsin,61 V. Ziegler,61 W. Park,62 M.V. Purohit,62

R.M. White,62 J. R. Wilson,62 A. Randle-Conde,63 S. J. Sekula,63 M. Bellis,64 P. R. Burchat,64 T. S. Miyashita,64

E.M. T. Puccio,64 M. S. Alam,65 J. A. Ernst,65 R. Gorodeisky,66 N. Guttman,66 D. R. Peimer,66 A. Soffer,66

S.M. Spanier,67 J. L. Ritchie,68 A.M. Ruland,68 R. F. Schwitters,68 B. C. Wray,68 J.M. Izen,69 X. C. Lou,69

F. Bianchi,70a,70b D. Gamba,70a,70b S. Zambito,70a,70b L. Lanceri,71a,71b L. Vitale,71a,71b F. Martinez-Vidal,72

A. Oyanguren,72 P. Villanueva-Perez,72 H. Ahmed,73 J. Albert,73 Sw. Banerjee,73 F. U. Bernlochner,73

H.H. F. Choi,73 G. J. King,73 R. Kowalewski,73 M. J. Lewczuk,73 T. Lueck,73 I.M. Nugent,73 J.M. Roney,73

R. J. Sobie,73 N. Tasneem,73 T. J. Gershon,74 P. F. Harrison,74 T. E. Latham,74 H. R. Band,75 S. Dasu,75

Y. Pan,75 R. Prepost,75 and S. L. Wu75

(BABAR Collaboration)

PHYSICAL REVIEW D 88, 052003 (2013)

1550-7998=2013=88(5)=052003(20) 052003-1 � 2013 American Physical Society

1Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie,CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France

2Departament ECM, Facultat de Fisica, Universitat de Barcelona, E-08028 Barcelona, Spain3aINFN Sezione di Bari, I-70126 Bari, Italy

3bDipartimento di Fisica, Università di Bari, I-70126 Bari, Italy4Institute of Physics, University of Bergen, N-5007 Bergen, Norway

5Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA6Institut für Experimentalphysik 1, Ruhr Universität Bochum, D-44780 Bochum, Germany

7University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z18Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom

9Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia10University of California at Irvine, Irvine, California 92697, USA

11University of California at Riverside, Riverside, California 92521, USA12University of California at Santa Barbara, Santa Barbara, California 93106, USA

13Institute for Particle Physics, University of California at Santa Cruz, Santa Cruz, California 95064, USA14California Institute of Technology, Pasadena, California 91125, USA

15University of Cincinnati, Cincinnati, Ohio 45221, USA16University of Colorado, Boulder, Colorado 80309, USA

17Colorado State University, Fort Collins, Colorado 80523, USA18Technische Universität Dortmund, Fakultät Physik, D-44221 Dortmund, Germany

19Institut für Kern- und Teilchenphysik, Technische Universität Dresden, D-01062 Dresden, Germany20Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France

21University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom22aINFN Sezione di Ferrara, I-44100 Ferrara, Italy

22bDipartimento di Fisica, Università di Ferrara, I-44100 Ferrara, Italy23INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy

24aINFN Sezione di Genova, I-16146 Genova, Italy24bDipartimento di Fisica, Università di Genova, I-16146 Genova, Italy

25Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India26Harvard University, Cambridge, Massachusetts 02138, USA

27Physikalisches Institut, Universität Heidelberg, Philosophenweg 12, D-69120 Heidelberg, Germany28Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany

29Imperial College London, London SW7 2AZ, United Kingdom30University of Iowa, Iowa City, Iowa 52242, USA

31Iowa State University, Ames, Iowa 50011-3160, USA32Johns Hopkins University, Baltimore, Maryland 21218, USA

33Laboratoire de l’Accélérateur Linéaire, Centre Scientifique d’Orsay, IN2P3/CNRS et Université Paris-Sud 11,B.P. 34, F-91898 Orsay Cedex, France

34Lawrence Livermore National Laboratory, Livermore, California 94550, USA35University of Liverpool, Liverpool L69 7ZE, United Kingdom

36Queen Mary, University of London, London E1 4NS, United Kingdom37Royal Holloway and Bedford New College, University of London, Egham, Surrey TW20 0EX, United Kingdom

38University of Louisville, Louisville, Kentucky 40292, USA39Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany

40University of Manchester, Manchester M13 9PL, United Kingdom41University of Maryland, College Park, Maryland 20742, USA

42Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA43McGill University, Montréal, Québec, Canada H3A 2T8

44aINFN Sezione di Milano, I-20133 Milano, Italy44bDipartimento di Fisica, Università di Milano, I-20133 Milano, Italy

45University of Mississippi, University, Mississippi 38677, USA46Physique des Particules, Université de Montréal, Montréal, Québec, Canada H3C 3J7

47aINFN Sezione di Napoli, I-80126 Napoli, Italy47bDipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy

48NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands49University of Notre Dame, Notre Dame, Indiana 46556, USA

50Ohio State University, Columbus, Ohio 43210, USA51University of Oregon, Eugene, Oregon 97403, USA52aINFN Sezione di Padova, I-35131 Padova, Italy

52bDipartimento di Fisica, Università di Padova, I-35131 Padova, Italy

J. P. LEES et al. PHYSICAL REVIEW D 88, 052003 (2013)

052003-2

53Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie Curie-Paris6,Université Denis Diderot-Paris7, F-75252 Paris, France

54aINFN Sezione di Perugia, I-06100 Perugia, Italy54bDipartimento di Fisica, Università di Perugia, I-06100 Perugia, Italy

55aINFN Sezione di Pisa, I-56127 Pisa, Italy55bDipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy

55cScuola Normale Superiore di Pisa, I-56127 Pisa, Italy56Princeton University, Princeton, New Jersey 08544, USA

57aINFN Sezione di Roma, I-00185 Roma, Italy57bDipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy

58Universität Rostock, D-18051 Rostock, Germany59Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom

60CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France61SLAC National Accelerator Laboratory, Stanford, California 94309, USA

62University of South Carolina, Columbia, South Carolina 29208, USA63Southern Methodist University, Dallas, Texas 75275, USA64Stanford University, Stanford, California 94305-4060, USA65State University of New York, Albany, New York 12222, USA

66School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel67University of Tennessee, Knoxville, Tennessee 37996, USA68University of Texas at Austin, Austin, Texas 78712, USA

69University of Texas at Dallas, Richardson, Texas 75083, USA70aINFN Sezione di Torino, I-10125 Torino, Italy

70bDipartimento di Fisica Sperimentale, Università di Torino, I-10125 Torino, Italy71aINFN Sezione di Trieste, I-34127 Trieste, Italy

71bDipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy72IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain

73University of Victoria, Victoria, British Columbia, Canada V8W 3P674Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

75University of Wisconsin, Madison, Wisconsin 53706, USA(Received 20 April 2013; published 9 September 2013)

We measure the mass difference, �m0, between theD�ð2010Þþ and the D0 and the natural linewidth, �,

of the transition D�ð2010Þþ ! D0�þ. The data were recorded with the BABAR detector at center-of-massenergies at and near the �ð4SÞ resonance, and correspond to an integrated luminosity of approximately477 fb�1. The D0 is reconstructed in the decay modes D0 ! K��þ and D0 ! K��þ��þ. For thedecaymodeD0!K��þweobtain� ¼ ð83:4� 1:7� 1:5Þ keV and�m0 ¼ ð145425:6� 0:6� 1:8Þ keV,where the quoted errors are statistical and systematic, respectively. For the D0 ! K��þ��þ mode weobtain � ¼ ð83:2� 1:5� 2:6Þ keV and �m0 ¼ ð145426:6� 0:5� 2:0Þ keV. The combined measure-ments yield � ¼ ð83:3� 1:2� 1:4Þ keV and �m0 ¼ ð145425:9� 0:4� 1:7Þ keV; the width is a factorof approximately 12 times more precise than the previous value, while the mass difference is a factor of

approximately 6 times more precise.

DOI: 10.1103/PhysRevD.88.052003 PACS numbers: 13.25.Ft, 14.40.Lb, 12.38.Qk, 12.39.Ki

I. INTRODUCTION

TheD�ð2010Þþ (D�þ) linewidth provides a window intoa nonperturbative regime of strong physics where thecharm quark is the heaviest meson constituent [1–3]. The

linewidth provides an experimental check of models oftheDmeson spectrum, and is related to the strong couplingof the D�þ to the D� system, gD�D�. In the heavy-quarklimit, which is not necessarily a good approximation forthe charm quark [4], this coupling can be related to theuniversal coupling of heavy mesons to a pion, ĝ. There isno direct experimental window on the correspondingcoupling in the B system, gB�B�, since there is no phasespace for the decay B� ! B�. However, the D and Bsystems can be related through ĝ, which allows thecalculation of gB�B�. The B

�B� coupling is needed for amodel-independent extraction of jVubj [5,6] and is pres-ently one of the largest contributions to the theoreticaluncertainty on jVubj [7].

*Deceased.†Present address:University ofTabuk,Tabuk71491, SaudiArabia.‡Also at Università di Perugia, Dipartimento di Fisica,

Perugia, Italy.§Present address: University of Huddersfield, Huddersfield

HD1 3DH, United Kingdom.∥Present address: University of South Alabama, Mobile,

Alabama 36688, USA.¶Also at Università di Sassari, Sassari, Italy.

MEASUREMENT OF THE D�ð2010Þþ NATURAL . . . PHYSICAL REVIEW D 88, 052003 (2013)

052003-3

http://dx.doi.org/10.1103/PhysRevD.88.052003

We study the D�þ ! D0�þ transition using the D0 !K��þ and D0 ! K��þ��þ decay modes to measurethe values of the D�þ linewidth, �, and the differencebetween the D�þ and D0 masses, �m0. The use of chargeconjugate reactions is implied throughout this paper. Theonly prior measurement of the width is � ¼ ð96� 4�22Þ keV by the CLEO collaboration where the uncertain-ties are statistical and systematic, respectively [8]. Thatmeasurement is based on a data sample correspondingto an integrated luminosity of 9 fb�1 and reconstructedD0 ! K��þ decays. In the present analysis, we have adata sample that is approximately 50 times larger. Thisallows us to apply tight selection criteria to reducebackground, and to investigate sources of systematicuncertainty with high precision.

The signal is described by a relativistic Breit-Wigner(RBW) function defined by

d�ðmÞdm

¼ m�D�D�ðmÞm0�ðm20 �m2Þ2 þ ðm0�TotalðmÞÞ2; (1)

where �D�D� is the partial width to D0�þ, m is the D0�þ

invariant mass, m0 is the invariant mass at the pole, and�TotalðmÞ is the total D�þ decay width. The partial width isdefined by

�D�D�ðmÞ ¼ ��F ‘D�ðp0ÞF ‘D�ðpÞ

�2�p

p0

�2‘þ1�m0

m

�; (2)

where F ‘¼1D� ðpÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ r2p2p is the Blatt-Weisskopf form

factor for a vector particle with radius parameter r anddaughter momentum p, and the subscript zero denotes aquantity measured at the pole [9,10]. The value of theradius is unknown, but for the charm sector it is expectedto be �1 GeV�1 [11]. We use the value r ¼ 1:6 GeV�1from Ref. [12] and vary this value as part of our inves-tigation of systematic uncertainties.

The full width at half maximum (FWHM) of the RBWline shape (� 100 keV) is much less than the FWHM ofthe almost Gaussian resolution function which describesmore than 99% of the signal (� 300 keV). Therefore, nearthe peak, the observed FWHM is dominated by the reso-lution function shape. However, the shapes of the resolu-tion function and the RBW differ far away from the poleposition. Starting (1.5–2.0) MeV from the pole position,and continuing to (5–10) MeVaway (depending on the D0

decay channel), the RBW tails are much larger. The signalrates in this region are strongly dominated by the intrinsiclinewidth, not the resolution functions, and the integratedsignals are larger than the integrated backgrounds. We usethe very different resolution and RBW shapes, combinedwith the good signal-to-background rate far from the peak,to measure � precisely.

The detailed presentation is organized as follows.Section II discusses the BABAR detector and the dataused in this analysis, and Sec. III describes the eventselection. Section IV discusses a correction to the detector

material model and magnetic field map. Section V detailsthe fit strategy, Sec. VI discusses and quantifies the sourcesof systematic uncertainty, and Sec. VII describes howthe results for the two D0 decay modes are combined toobtain the final results. Finally, the results are summarizedin Sec. VIII.

II. THE BABAR DETECTOR AND DATA

This analysis is based on a data sample correspondingto an integrated luminosity of approximately 477 fb�1recorded at and 40 MeV below the �ð4SÞ resonance bythe BABAR detector at the PEP-II asymmetric energy eþe�collider [13]. The BABAR detector is described in detailelsewhere [14,15], so we summarize only the relevantcomponents below. Charged particles are measured witha combination of a 40-layer cylindrical drift chamber(DCH) and a 5-layer double-sided silicon vertex tracker(SVT), both operating within the 1.5-T magnetic fieldof a superconducting solenoid. Information from a ring-imaging Cherenkov detector is combined with specificionization (dE=dx) measurements from the SVT andDCH to identify charged kaon and pion candidates.Electrons are identified, and photons measured, with aCsI(Tl) electromagnetic calorimeter. The return yoke ofthe superconducting coil is instrumented with trackingchambers for the identification of muons.

III. EVENT SELECTION

We reconstruct continuum-produced D�þ ! D0�þs de-cays in the two Cabibbo-favored channels D0 ! K��þand D0 ! K��þ��þ. The pion from the D�þ decay iscalled the ‘‘slow pion’’ (denoted �þs ) because of thelimited phase space available. The mass difference ofthe reconstructed D�þ and D0 is denoted as �m [e.g.mðK��þ�þs Þ �mðK��þÞ for the D0 ! K��þ channel].The resolution in �m is dominated by the resolution of the�þs momentum, especially the uncertainty of its directiondue to Coulomb multiple scattering. The selection criteriafor the individualD0 channels are detailed below; however,both modes have the same D�þ requirements. Theselection criteria were chosen to enhance the signal-to-background ratio (S/B) to increase the sensitivity to thelong RBW tails in the �m distribution; we have not opti-mized the criteria for statistical significance. Because thisanalysis depends on the RBW tails, we pay particularattention to how the selection criteria affect the tail regions.The entire decay chain is fit using a kinematic fitter with

geometric constraints at each vertex and the additionalconstraint that the D�þ emerges from the luminous region,also referred to as the beam spot. The confidence level ofthe �2 for this fit must be greater than 0.1%. In addition, theconfidence level for the �2 from fitting the D0 daughtertracks to a common vertex must be at least 0.5%.These confidence level selections reduce the set of final


052003-4

candidates by approximately 2.1%. The beam spot con-straint improves the �m resolution by a factor of 2.5,primarily because it constrains the direction of the �þs . Ifthere is more than one D�þ candidate in the event, wechoose the one with the highest full decay chain confidencelevel. The reconstructed D0 mass must be within the range1.86 to 1.87 GeV. The mass difference between the D�þand D0 is required to satisfy �m< 0:17 GeV. A largeamount of the combinatorial background is removed byrequiring p�ðD�þÞ> 3:6 GeV, where p� is the momentummeasured in the eþe� center-of-mass frame for the event.

To select well-measured slow pions we require that the�þs tracks have at least 12 measurements in the DCH andhave at least six SVT measurements with at least two inthe first three layers. For both D0 ! K��þ and D0 !K��þ��þ, we apply particle identification (PID)requirements to the K and � candidate tracks. To selectcandidates with better tracking resolution, and conse-quently improve the resolution of the reconstructedmasses, we require that D0 daughter tracks have at least21 measurements in the DCH and satisfy the same SVTmeasurement requirements for the slow pion track.Figure 1 illustrates the signal region distributions for threedisjoint sets of D0 ! K��þ candidates: those passing alltracking requirements (narrowest peak), those otherwisepassing all tracking requirements but failing the SVT hitrequirements (intermediate peak), and those otherwisepassing all tracking requirements but failing the require-ment that both D0 daughter tracks have at least 21 hits inthe DCH and the �þs track has at least 12 hits in the DCH(widest peak). The nominal sample (narrowest peak) hasbetter resolution and S/B than candidates that fail the strict

tracking requirements. We reduce backgrounds from otherspecies of tracks in our slow pion sample by requiring thatthe dE=dx values reported by the SVT and DCH be con-sistent with the pion hypothesis. Figure 2 shows the �mdistribution for candidates otherwise passing cuts, but inwhich the slow pion candidate fails either the SVTor DCHdE=dx requirement. The dE=dx selections remove protonsfrom slow pion interactions in the beam pipe and detectormaterial as well as electrons from the D�0 decay chaindiscussed below. As shown in Fig. 2, while this require-ment removes much more signal than background, the S/Bratio of the removed events is distinctly worse than that inthe final sample.The Dalitz decay �0 ! �eþe� produces background

where we misidentify a positron as a �þs . We eliminatesuch candidates by reconstructing a candidate eþe� pairand combining it with a �. If the eþe� vertex is within theSVT volume and the invariant mass is in the range115 MeV

poorly models the data. The MC is a cocktail of q �q and‘þ‘� sources where q ¼ u, d, s, c, b and ‘ ¼ e,�, �. Thesimulation does not accurately replicate the momentumdistributions observed in data at very high and lowD�þ momentum values, so we require that 3:6 GeV<p�ðD�þÞ< 4:3 GeV and that the laboratory momentum

of the slow pion be at least 150 MeV. In an independentsample of K0S ! ��þ decays, the reconstructed K0S massis observed to vary as a function of the polar angle � of theK0S momentum measured in the laboratory frame withrespect to the electron beam axis. We define the acceptanceangle to reject events where any of the daughter tracks ofthe D�þ has cos � � 0:89 to exclude the very-forwardregion of the detector. This criterion reduces the finaldata samples by approximately 10%.The background level in theD0 ! K��þ��þ mode is

much higher than that inD0 ! K��þ, and sowe requireD0daughter charged tracks to satisfy stricter PID requirements.The higher background arises because theD0 mass is on thetail of the two-body K��þ invariant mass distribution ex-pected in a longitudinal phase spacemodel, however it is nearthe peak of the four-body K��þ��þ invariant massdistribution [16]. In addition, there is more random combi-natorial background in the four-track D0 ! K��þ��þmode than in the two-track D0 ! K��þ mode.The initial fit to the D0 ! K��þ��þ validation

signal MC sample had a bias in the measured value ofthe D�þ width. An extensive comparison revealed thatthe bias originated from regions of phase space that theMC generator populated more frequently than the data.Evidently, there are amplitudes that suppress these

m [GeV]∆0.14 0.145 0.15 0.155 0.16 0.165

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FIG. 3. Events with D�þ candidates from D0 ! K��þ thatpass all selection criteria, but the slow pion candidate is identi-fied by the algorithms as either a photon conversion in thedetector material or a �0 Dalitz decay.

0

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FIG. 4 (color online). Illustrations of the ðm0;�m0Þ system in (a) MC with the D�þ correctly reconstructed, (b) MC with the slowpion and aD0 daughter pion swapped during reconstruction, and (c) in data. The majority of correctly reconstructed decays are locatedoutside of the shown ðm0;�m0Þ range.


052003-6

structures in the data, that are neither known nor includedin the MC generator. We avoid the regions where theMC disagrees with the data by rejecting a candidate ifeither ðm2ð�þ�þÞ99:5% pure), which is shownin Fig. 5. This sample is used to determine fractionalcorrections to the overall magnetic field and to the energy

losses in the beam pipe (Ebmploss ) and, separately, in the SVT(Esvtloss). The points represented as open squares in Fig. 6show the strong dependence of the reconstructed K0S masson laboratory momentum. Adjusting only the estimatedenergy losses and detector material flattens the distribution,but there is still a remaining discrepancy. This discrepancyis shown by the open squares in Fig. 6 at high momentumand indicates an overall momentum scale problem. Thesetwo effects lead us to consider corrections to the laboratorymomentum and energy of an individual track of the form

p ! pð1þ aÞ; E ! Eþ bbmpEbmploss þ bsvtEsvtloss; (3)

where the initial energy losses are determined by theKalman filter based on the material model. To apply thecorrection to a pion track, the magnitude of the momentumis first recalculated using the pion mass hypothesis and thecorrected energy as shown in Eq. (3) where the energy

losses (Ebmploss and ESVTloss ) are taken from the original Kalman

) [MeV]-π+πm(475 480 485 490 495 500 505 510 515 520

Eve

nts

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1 M

eV

0

500

1000

1500

2000

2500

FIG. 5. Sample of K0S ! �þ�� candidates from D�þ !D0�þs ! ðK0S��þÞ�þs decay where the K0S daughter pionssatisfy the same tracking criteria as the slow pions of the D�þanalysis.


052003-7

fit. Then, the momentum is scaled by the parameter ashown in Eq. (3) and the energy of the particle is recalcu-lated assuming the pion mass hypothesis. The order ofthese operations, correcting the energy first and then themomentum, or vice versa, has a negligibly small effect onthe calculated corrected invariant mass. After both piontracks’ momenta are corrected the invariant mass is calcu-lated. Then the sample is separated into 20 intervals of K0Smomentum. Figure 6 shows mð�þ��Þ as a function ofthe slower pion laboratory momentum and illustratesthat the momentum dependence of the original sample(open squares) has been removed after all of the correc-tions (closed circles). We determine the best set of correc-tion parameters to minimize the �2 of the bin-by-bin massdifference between the �þ�� invariant mass and thecurrent value of the K0S mass (mPDGðK0SÞ � 1�PDG ¼497:614� 0:024 MeV) [18].

To estimate the systematic uncertainty in values mea-sured from corrected distributions, we find new parametervalues by tuning the �þ�� invariant mass to the nominalK0S mass shifted up and down by one standard deviation.These three sets of correction parameters are listed inTable I. The resulting average reconstructed K0S massesafter correction are 497:589� 0:007 MeV, 497:612�0:007 MeV, and 497:640� 0:007 MeV for target massesmPDGðK0SÞ � 1�PDG, mPDGðK0SÞ, and mPDGðK0SÞ þ 1�PDG,respectively. As these average values are so well separatedwe do not include additional systematic uncertainties fromparameters that could describe the central value. The sys-tematics studies of fit result variations in disjoint subsam-ples of laboratory momentum remain sensitive to ourimperfect correction model.

The best-fit value of a ¼ 0:00030 corresponds to anincrease of 4.5 Gauss on the central magnetic field. Thisis larger than the nominal 2 Gauss sensitivity of themagnetic field mapping [14]. However, the azimuthal

dependence of �m0 (discussed in Sec. VI) indicates thatthe accuracy of the mapping may be less than originallythought.The momentum dependence of �m0 in the initial results

is ascribed to underestimating the dE=dx loss in the beampipe and SVT, which we correct using the factors bbmp(1.8%) and bSVT (5.9%). Typical dE=dx losses for a mini-mum ionizing particle with laboratory momentum 2 GeVtraversing the beam pipe and SVT at normal incidence are4.4 MeV. The corrections are most significant for low-momentum tracks. However, the corrections are appliedto all D�þ daughter tracks, not just to the slow pion. Themomentum dependence is eliminated after the correctionsare applied. All fits to data described in this analysis areperformed using masses and �m values calculated usingcorrected 4-momenta. The MC tracks are not correctedbecause the same field and material models used to propa-gate tracks are used during their reconstruction.

V. FIT METHOD

To measure � we fit the �m peak (the signal) with arelativistic Breit-Wigner (RBW) function convolved with aresolution function based on a GEANT4 MC simulation ofthe detector response [19]. As in previous analyses [8],we approximate the total D�þ decay width �TotalðmÞ ��D�D�ðmÞ, ignoring the electromagnetic contributionfrom D�þ ! Dþ�. This approximation has a negligibleeffect on the measured values as it appears only in thedenominator of Eq. (1). For the purpose of fitting the �mdistribution we obtain d�ð�mÞ=d�m from Eqs. (1) and (2)by making the substitution m ¼ mðD0Þ þ �m, wheremðD0Þ is the current average mass of the D0 meson [18].Our fitting procedure involves two steps. In the first step

we model the resolution due to track reconstruction byfitting the �m distribution for correctly reconstructedMC events using a sum of three Gaussians and a functionto describe the non-Gaussian component. The second stepuses the resolution shape from the first step and convolvesthe Gaussian components with a relativistic Breit-Wignerof the form in Eq. (1) to fit the �m distribution in data, andthus measure � and�m0. We fit the�m distribution in data

TABLE I. Energy-loss and momentum correction parametersof Eq. (3) which remove the momentum dependence of thereconstructed K0S mass shown in Fig. 6. The nominal parametersshift the average reconstructed masses to be the PDG meanvalue, also shown in Fig. 6. To estimate the associated systematicuncertainty, the procedure was repeated to give average recon-structed K0S masses �1�PDG from the nominal value.

Nominal For systematics

mPDGðK0SÞ mPDG þ 1�PDG mPDG � 1�PDGa 0.00030 0.00031 0.00019bbmp 0.0175 0.0517 0.0295bsvt 0.0592 0.0590 0.0586

[GeV]πLab momentum of slower -110 1

) [M

eV]

- π+ πm

(

497.1

497.2

497.3

497.4

497.5

497.6

497.7

497.8 Original Corrected σ 1± mass 0SPDG K

FIG. 6 (color online). Mass value of the K0S obtained by fittingthe invariant �þ�� mass distribution shown as a function of theslower pion laboratory momentum before (open squares) andafter (closed circles) all energy-loss and momentum correctionshave been applied. Note that the horizontal scale is logarithmic.


052003-8

and MC from the kinematic threshold to �m ¼0:1665 GeV using a binned maximum likelihood fit andan interval width of 50 keV. Detailed results of the fits arepresented in the Appendix.

A. Modeling experimental resolution

We generate samples of D�þ decays with a linewidth of0.1 keV, so that all of the observed spread is due toreconstruction effects. The samples are approximately 5times the size of the corresponding samples in data. Thenon-Gaussian tails of the distribution are from events inwhich the �s decays to a � in flight and where coordinatesfrom both the � and � segments are used in track recon-struction. Accounting for these non-Gaussian eventsgreatly improves the quality of the fit to data near the�m peak.

We fit the �m distribution of the MC events with thefunction

fNGSNGð�m; q; �Þ þ ð1� fNGÞ½f1Gð�m;�1; �1Þþ f2Gð�m;�2; �2Þ þ ð1� f1 � f2ÞGð�m;�3; �3Þ�;

(4)

where the Gð�m;�i; �iÞ are Gaussian functions and fNG,f1, f2 are the fractions allotted to the non-Gaussian com-ponent and the first and second Gaussian components,respectively. The function describing the non-Gaussiancomponent of the distribution is

SNGð�m; q; �Þ ¼ �muqe�u; (5)where u � ð�m=�mthresÞ2 � 1 and �mthres ¼ m� is thekinematic threshold for the D�þ ! D0�þ process. For�m

and is not convolved with the RBW. The relative contri-bution of SNG is small and the results from the fits to thevalidation signal MC samples are unbiased withoutconvolving this term. We fit the data using the function

P ð�m; ;�;�m0; cÞ

¼ fS Sð�m; ;�;�m0ÞRSð�mÞdð�mÞ þ ð1� fSÞBð�m; cÞRBð�mÞdð�mÞ ;

(6)

where fS is the fraction of signal events, S is the signalfunction

Sð�mÞ ¼ RBW ð1� fMCNG Þ½fMC1 Gð�m;�MC1��mMC0 ; �MC1 ð1þ ÞÞ þ fMC2 Gð�m;�MC2��mMC0 ; �MC2 ð1þ ÞÞ þ ð1� fMC1 � fMC2 Þ

Gð�m;�MC3 � �mMC0 ; �MC3 ð1þ ÞÞ�þ fMCNGSNGð�m; qMC; �MCÞ; (7)

and B is the background function

Bð�mÞ ¼ �m ffiffiffiup ecu; (8)where, again, u � ð�m=�mthresÞ2 � 1. The nominal RBWfunction has a pole position located at m ¼ �m0 þmðD0Þand natural linewidth �. The Gaussian resolution functionsconvolved with the RBW have centers offset from zeroby small amounts determined from MC, �i � �mMC0(see Table VII in the Appendix). The widths determinedfrom MC, �MCi , are scaled by (1þ ) where is a com-mon, empirically determined constant which accountsfor possible differences between resolutions in data andsimulation. As indicated in Eq. (7), the parameters allowedto vary in the fit to data are the scale factor (1þ ), thewidth �, pole position �m0, and background shapeparameter c. The validation of the fit procedure isdiscussed in Sec. VIC.

Figure 8 shows the fits to data for both D0 decay modes.The total PDF is shown as the solid curve, the convolvedRBW-Gaussian signal as the dashed curve, and the thresh-old background as the dotted curve. The normalized resid-uals show the good agreement between the data and themodel. Table II summarizes the results of the fits to data forthe two modes. The covariance and correlation matrices foreach mode are presented in Tables XII, XIII, XIV, and XVin the Appendix. The tails of the RBW are much longerthan the almost Gaussian resolution function. The resolu-tion functions determined from the fits to MC drop byfactors of more than 1000 near �m � 147 MeV withrespect to the peak. At �m ¼ 148 MeV the resolutionfunctions have dropped by another factor of 10 and aredominated by the SNG component. The resolution func-tions used in fitting the data allow the triple-Gaussian partof the resolution function to scale by (1þ ), but the eventsobserved above 148 MeV are predominantly signal events

from the RBW tails and background. The signal from azero-width RBW would approach three events per bin(see Fig. 7). The observed signal levels are of order 30events per bin (see Fig. 8). Table II also shows the fittedS/B at the peak and in the �m tail on the high side of thepeak. The long non-Gaussian tail of the RBW is requiredfor the model to fit the data so well.As the observed FWHM values from the resolu-

tion functions are greater than the intrinsic linewidth,the observed widths of the central peaks determine the

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FIG. 8 (color online). The results of the fits to data for each D0

decay mode. The fitted parameter values are summarized inTable II. The solid curve is the sum of the signal (dashed curve)and background (dotted curve) PDFs. The total PDF and signalcomponent are visually indistinguishable in the peak region.


052003-10

values of . The scale factor, (1þ ), allows theresolution functions to expand as necessary to describethe distribution in real data. As one naively expects, thefitted values of the scale factor are strongly anticorre-lated with the values for � (the typical correlationcoefficient is �0:85).

VI. SYSTEMATIC UNCERTAINTIES

We estimate systematic uncertainties associated withinstrumental effects by looking for large variations ofresults in disjoint subsets. The systematic uncertaintiesassociated with our fit procedure are estimated using avariety of techniques. These methods are summarized inthe following paragraphs and then discussed in detail.

To estimate systematic uncertainties from instrumentaleffects, we divide the data into disjoint subsets correspond-ing to intervals of laboratory momentum, p, of the D�þ,

azimuthal angle,�, of theD�þ in the laboratory frame, andreconstructed D0 mass. In each of these variables wesearch for variations greater than those expected fromstatistical fluctuations.After the corrections to the material model and magnetic

field, the laboratory momentum dependence of the RBWpole position is all but eliminated. We find that � does notdisplay an azimuthal dependence, however �m0 does.Neither � nor �m0 displays a clear systematic shape withreconstructed D0 mass.The uncertainties associated with the various parts of the

fit procedure are investigated in detail. We vary the parame-ters of the resolution function in Eq. (4) according to thecovariance matrix reported by the fit to estimate systematicuncertainty of the resolution shape. Changing the end pointfor the fit estimates a systematic uncertainty associated withthe shape of the background function. We also change thebackground shape near threshold. To estimate the uncer-tainty in the Blatt-Weisskopf radius we model the D�þ as apointlike particle. We fit MC validation samples to estimatesystematic uncertainties associated with possible biases.Finally, we estimate possible systematic uncertainties dueto radiative effects. All of these uncertainties are estimatedindependently for theD0!K��þ andD0!K��þ��þmodes, and are summarized in Table III.

A. Systematics using disjoint subsets

We chose to carefully study laboratory momentum,reconstructed D0 mass, and azimuthal angle � in orderto search for variations larger than those expected fromstatistical fluctuations. For each disjoint subset, we usethe resolution function parameter values and �m0 offsetdetermined from the corresponding MC subset.If the fit results from the disjoint subsets are compatible

with a constant value, in the sense that �2=� � 1 where �

TABLE II. Summary of the results from the fits to data for theD0 ! K��þ and D0 ! K��þ��þ channels (statisticaluncertainties only); S/B is the ratio of the convolved signalPDF to the background PDF at the given value of �m, and �is the number of degrees of freedom.

Parameter D0 ! K� D0 ! K��Number of signal events 138536� 383 174297� 434� (keV) 83:3� 1:7 83:2� 1:5Scale factor, (1þ ) 1:06� 0:01 1:08� 0:01�m0 (keV) 145425:6� 0:6 145426:6� 0:5Background shape, c �1:97� 0:28 �2:82� 0:13S/B at peak

(�m ¼ 0:14542 ðGeVÞ)2700 1130

S/B at tail

(�m ¼ 0:1554 ðGeVÞ)0.8 0.3

�2=� 574=535 556=535

TABLE III. Summary of systematic uncertainties with correlation, , between theD0 ! K��þand D0 ! K��þ��þ modes. The K��þ and K��þ��þ invariant masses are denoted bymðD0recoÞ. The methods used to calculate or define the correlations are described in Sec. VID. Thetotal systematic uncertainties are calculated according to the procedure defined in Sec. VII.

�sysð�Þ [keV]

�sysð�m0Þ [keV]

Source K� K�� K� K��

Disjoint p variation 0.88 0.98 0.47 0.16 0.11 0.28

Disjoint mðD0recoÞ variation 0.00 1.53 0.56 0.00 0.00 0.22Disjoint azimuthal variation 0.62 0.92 �0:04 1.50 1.68 0.84Magnetic field and material model 0.29 0.18 0.98 0.75 0.81 0.99

Blatt-Weisskopf radius 0.04 0.04 0.99 0.00 0.00 1.00

Variation of resolution shape parameters 0.41 0.37 0.00 0.17 0.16 0.00

�m fit range 0.83 0.38 �0:42 0.08 0.04 0.35Background shape near threshold 0.10 0.33 1.00 0.00 0.00 0.00

Interval width for fit 0.00 0.05 0.99 0.00 0.00 0.00

Bias from validation 0.00 1.50 0.00 0.00 0.00 0.00

Radiative effects 0.25 0.11 0.00 0.00 0.00 0.00

Total 1.5 2.6 1.7 1.9


052003-11

denotes the number of degrees of freedom, we assignno systematic uncertainty. However, if we find �2=� > 1and do not determine an underlying model which mightbe used to correct the data, we ascribe an uncertaintyusing a variation on the scale factor method used by theParticle Data Group (see the discussion of unconstrainedaveraging [18]). The only sample which we do not fit to aconstant is that for�m0 in intervals of azimuthal angle. Wediscuss below how we estimate the associated systematicuncertainty.

In our version of this procedure, we determine a factorthat scales the statistical uncertainty to the total uncer-tainty. The remaining uncertainty is ascribed to unknowndetector issues and is used as a measure of systematicuncertainty according to

�sys ¼ �statffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2 � 1

p; (9)

where the scale factor is defined as S2 ¼ �2=�. The �2statistic gives a measure of fluctuations, including thoseexpected from statistics, and those from systematic effects.Once we remove the uncertainty expected from statisticalfluctuations, we associate what remains with a possiblesystematic uncertainty.

We expect that �2=� will have an average value of unityif there are no systematic uncertainties that distinguish onesubset from another. If systematic deviations from onesubset to another exist, then we expect that �2=� will begreater than unity. Even if there are no systematic varia-tions from one disjoint subset to another, �2=� will ran-domly fluctuate above 1 about half of the time. To beconservative, we assume that any observation of �2=� >1 originates from a systematic variation from one disjointsubset to another. This approach has two weaknesses. Ifused with a large number of subsets it could hide realsystematic uncertainties. For example, if instead of 10subsets we chose 1000 subsets, the larger statistical un-certainties wash out any real systematic variation. Also, ifused with a large number of variables, about half thedisjoint sets will have upward statistical fluctuations,even in the absence of any systematic variation. We havechosen to use only three disjoint sets of events, andhave divided each into ten subsets to mitigate the effectsof such problems.

We choose the range for each subset to have approxi-mately equal statistical sensitivity. In each subset ofeach variable we repeat the full fit procedure (determinethe resolution function from MC and fit data floating ,�, �m0, and c). Figures 9(a) and 9(b) show the fit resultsin subsets of laboratory momentum for � and �m0,respectively. Neither D0 mode displays a systematicpattern of variation; however, we assign small uncertain-ties for each channel using Eq. (9). Similarly, Figs. 9(c)and 9(d) show the results in ranges of reconstructed D0

mass for � and �m0. While neither mode displays anobvious systematic pattern of variation, the width for the

K��þ��þ mode is assigned its largest uncertainty of1.53 keV using Eq. (9).Figures 9(e) and 9(f) show � and �m0, respectively, in

subsets of azimuthal angle. In this analysis we haveobserved sinusoidal variations in the mass values forD0 !K��þ, D0 ! K��þ��þ, and K0S ! �þ��, so theclear sinusoidal variation of �m0 was anticipated. Theimportant aspect for this analysis is that, for such devia-tions, the average value is unbiased by the variation in �.For example, the average value of the reconstructed K0Smass separated into intervals of � is consistent with themass value integrating across the full range. The widthplots do not display azimuthal dependencies, but eachmode has �2=� > 1 and is assigned a small systematicuncertainty using Eq. (9). The lack of sinusoidal variationof � with respect to � is notable because �m0 (which usesreconstructedDmasses) shows a clear sinusoidal variation.The results for the D0 ! K��þ and D0 ! K��þ��þdata sets are highly correlated, and shift together. The signsand phases of the variations of �m0 agree with thoseobserved for D0 ! K��þ, D0 ! K��þ��þ, andK0S ! �þ��. We take half of the amplitude obtainedfrom the sinusoidal fit shown on Fig. 9(f) as an estimateof the uncertainty. An extended investigation revealed thatat least part of this dependence originates from small errorsin the magnetic field from the map used in track recon-struction. There is some evidence that during the fieldmapping (see Ref. [14]) the propeller arm on which theprobes were mounted flexed, which mixed the radial andangular components of the magnetic field.The FWHM values of the resolution functions vary by

about 8% for each decay channel. For D0 ! K��þ theFWHM ranges from 275 to 325 keV for the 30 disjointsubsets studied. The FWHM of the D0 ! K��þ��þresolution function ranges are 310 to 350 keV for the 30disjoint subsets studied. Figure 10 shows the values of thescale factor corresponding to the values of � and �m0shown in Fig. 9.

B. Additional systematics

We estimate the uncertainty associated with the correc-tion parameters for the detector material model and mag-netic field by examining the variation between thenominal parameter values and those obtained by tuningto the mPDGðK0SÞ � 1�PDG mass values [18]. The widthmeasured from the D0 ! K��þ mode fluctuates equallyaround the value from the fit using the nominal correctionparameters. We take the larger of the differences andassign an uncertainty of 0.29 keV. The value of �m0 forthis mode fluctuates symmetrically around the nominalvalue and we assign an uncertainty of 0.75 keV. The widthmeasured from the D0 ! K��þ��þ fluctuates asym-metrically around the nominal value, and we use thelarger difference to assign an uncertainty of 0.18 keV.The value of �m0 for this mode fluctuates symmetrically


052003-12

around the nominal value, and we assign an uncertainty of0.81 keV.

We use the Blatt-Weisskopf radius r ¼ 1:6 GeV�1(� 0:3 fm) [12]. To estimate the systematic effect due tothe choice of r we refit the distributions treating theD�þ asa pointlike particle (r ¼ 0). We see a small shift of �,which we take as the estimate of the uncertainty, and aneffect on the RBW pole position that is a factor of 100smaller than the fit uncertainty, which we neglect.

We determine the systematic uncertainty associated withthe resolution function by refitting the data with variations

of its parametrization. We take the covariance matrixfrom the fit to MC resolution samples for each mode(see Tables VIII and X in the Appendix) and use it togenerate 100 variations of these correlated Gaussian-distributed shape parameters. We use these generatedvalues to refit the data, and take the root-mean-squareddeviation of the resulting fit values as a measure of system-atic uncertainty. This process implicitly accounts for theuncertainty associated with the reconstruction offset.Our choice of fit range in �m is somewhat arbitrary,

so we study the effect of systematically varying its end

p [GeV]1 2 3 4 5 6 7

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datasets: 0.47π and K3πCorrelation of K

bin fitπK bin fitπK3 weighted avg. per bin nom. fitπK nom. fitπK3 weighted avg. all bins

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) [GeV]0m(D1.86 1.862 1.864 1.866 1.868 1.87

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Sinusoidal fit to w. avg.

FIG. 9 (color online). The values of � (left) and �m0 (right) obtained from fits to data divided into ten disjoint subsets in laboratorymomentum p (top row), reconstructed D0 mass (center row), and azimuthal angle (bottom row). The quantities p and � are defined bythe D�þ momentum. Each point represents an individual fit and each horizontal line is the nominal fit result (i.e. integrating over thevariable). The correlation value of � (or �m0) measured from the D

0 ! K��þ and D0 ! K��þ��þ samples for each of thevariables chosen is given above each plot. The widths from the nominal fits and the weighted average agree well and the correspondinglines are visually indistinguishable.


052003-13

point by repeating the fit procedure every 1 MeV fromthe nominal fit end point, �m ¼ 0:1665 GeV, down to�m ¼ 0:1605 GeV. Altering the end point of the fitchanges the events associated with the RBW tails andthose associated with the continuum background. Eachstep down allows the background to form a differentshape, which effectively estimates an uncertainty in thebackground parametrization. Values below �m ¼0:16 GeV are too close to the signal region to provide areasonable choice of end point. There is no clear wayto estimate the associated systematic uncertainty, so wetake the largest deviation from the nominal fit as aconservative estimate.

The shape of the background function in Eq. (8) isnominally determined only by the parameter c and theresiduals in Figs. 8(a) and 8(b) show signs of curvatureindicating possible systematic problems with the fits.Changing the end points over the range considered changesthe values of c substantially from �1:97 to �3:57, andsome fits remove all hints of curvature in the residuals plot.We also examine the influence of the background parame-trization near threshold by changing

ffiffiffiu

pin Eq. (8) to u0:45

and u0:55. The value of the fractional power controls theshape of the background between the signal peak andthreshold. For example, at �m ¼ 0:142 GeV changingthe power from 0.5 to 0.45 and 0.55 varies the background

function by þ18% and �15%, respectively. The RBWpole position is unaffected by changing the backgrounddescription near threshold while � shifts symmetricallyaround its nominal values. We estimate the uncertaintydue to the description of the background function nearthreshold by taking the average difference to the nominalresult.In the binned maximum likelihood fits we nominally

choose an interval width of 50 keV. As a systematiccheck, the interval width was halved and the fits to thedata were repeated. The measured � and �m0 values forboth modes are identical except for the width measured inthe D0 ! K��þ��þ decay mode. We take the fulldifference as the systematic uncertainty for the choice ofinterval width.

C. Fit validations

We generate signal MC with � ¼ 88 keV and �m0 ¼0:1454 GeV. The background is taken from a MC cocktailand paired with the signal in the same ratio as from thecorresponding fits to data. Fits to both decay modes de-scribe the validation samples well. The fit results aresummarized in Table IV. We observe a small bias in thefitted width for the D0 ! K��þ��þ mode. We takethe full difference between the fitted and generated valueof the width and assign a 1.5 keV error.

p [GeV]1 2 3 4 5 6 7

) s

cale

fac

tor

∈(

1 +

0.95

1

1.05

1.1

1.15

1.2

1.25 bin fitπK bin fitπK3 full fitπK full fitπK3

(a)

) [GeV]0m(D

1.86 1.862 1.864 1.866 1.868 1.87

) s

cale

fac

tor

∈(

1 +

0.95

1

1.05

1.1

1.15

1.2


(b)


) s

cale

fac

tor

∈(

1 +

0.95

1

1.05

1.1

1.15

1.2


(c)

FIG. 10 (color online). The values of the scale factor (1þ ) obtained from fits to data divided into ten disjoint subsets inlaboratory momentum p, reconstructed D0 mass, and azimuthal angle. The quantities p and � are defined by the D�þ laboratorymomentum. Each point represents an individual fit and each horizontal line is the nominal fit result (i.e. integrating over thevariable).


052003-14

We also investigated the uncertainty due to radiativeeffects by examining the subset of these events generatedwithout PHOTOS [20]. The values of the RBW pole areidentical between the fits to the total validation signalMC sample and the subsets, so we do not assign a system-atic uncertainty to the poles for radiative effects. Thewidths measured in each mode show a small differenceto the results from the nominal validation sample. We takehalf of this difference as a conservative estimate of thesystematic uncertainty associated with radiative effects.

D. Determining correlations

The fourth and seventh columns in Table III list thecorrelations between the D0 ! K��þ and D0 !K��þ��þ systematic uncertainties. These correlationsare required to use information from both measurements tocompute the average. The correlations in laboratory mo-mentum, reconstructed D0 mass, and azimuthal angle dis-joint subsets are calculated by finding the correlationbetween the ten subsets of D0 ! K��þ and D0 !K��þ��þ for each of the variables. In a similar waywe can construct data sets using the sets of correctionparameters for magnetic field, detector material model,and the �m fit range. We assume no correlation for theresolution shape parameters and the validation shifts, whichare based on the individual reconstructions. Our studiesshow that the values chosen for the Blatt-Weisskopf radiusand interval width affect each mode identically, so weassume that they are completely correlated.

E. Consistency checks

In addition to the investigations into the sources ofsystematic uncertainty, we also perform a number of con-sistency checks. These checks are not used to assess sys-tematics, nor are they included in the final measurements,but serve to reassure us that the experimental approach andfitting technique behave in reasonable ways. First, welower the p� cut from 3.6 to 2.4 GeV. This allows morebackground and tracks with poorer resolution, but thestatistics increase by a factor of 3. Correspondingly, thesignal-to-background ratios measured at the peak and inthe tails decrease by approximately a factor of 3. The fitresults for this larger data set are consistent with the

nominal fit results. The second consistency check widensthe reconstructed D0 mass window from 10 to 30 MeV.Again, this increases the number of background events andimproves statistical precision with central values that over-lap with the nominal fit results. Finally, we fix the scalefactor in the fit to data to report statistical uncertainties on� similar to those in the measurement by CLEO [8]. Ourreported ‘‘statistical’’ uncertainties on � are from a fit inwhich floats. As expected, there is a strong negativecorrelation between and � with ð�; Þ � �0:85. Ifless of the spread in the data is allotted to the resolutionfunction then it must be allotted to the RBW width, �. Werefit the D0 ! K��þ and D0 ! K��þ��þ samplesfixing to the value from the fit where it was allowed tofloat. This effectively maintains the same global minimumwhile decoupling the uncertainty in � from . The statis-tical uncertainty on the width decreases from 1.7 to 0.9 keVfor the D0 ! K��þ decay mode and from 1.5 to 0.8 keVfor the D0 ! K��þ��þ decay mode.

VII. COMBINING RESULTS

Using the correlations shown in Table III and the formal-ism briefly outlined below, we determine the values for thecombined measurement. For each quantity, � and �m0, wehave a measurement from the D0 ! K��þ and D0 !K��þ��þ modes. So, we start with a 2 2 covariancematrix

V ¼ �2K� covðK�;K��Þ

covðK�;K��Þ �2K��

!

¼�2K�;stat þ �2K�;sys

Pi i�K�;i�K��;iP

i i�K�;i�K��;i �2K��;stat þ �2K��;sys

0@

1A;

(10)

where i is an index which runs over the sources of system-atic uncertainty. In the final step we expand the notation toexplicitly show that the diagonal entries incorporate thefull systematic uncertainty and that the statistical uncer-tainty for the individual measurements plays a part indetermining the weights. The covariance matrices are cal-culated using Table III and the individual measurements.From the covariance matrix we extract the weights, w, forthe best estimator of the mean and variance usingwi ¼

PkV

�1ik =

PjkV

�1jk :

w� ¼wK�

wK��

!¼ 0:650

0:350

!; (11)

w�m0 ¼wK�

wK��

!¼ 0:672

0:328

!: (12)

The weights show that the combined measurement isdominated by the cleaner D0 ! K��þ mode. The totaluncertainty can be expressed as

TABLE IV. Summary of results of the fits to the D0 ! K��þandD0 ! K��þ��þ validation MC samples. The width fromthe D0 ! K��þ��þ decay mode has a small bias, which wetake as a systematic uncertainty.

Fit value Generated D0 ! K� D0 ! K�� [keV] 88.0 88:5� 0:8 89:5� 0:6scale factor, 1þ 1.0 1:003� 0:004 1:000� 0:001�m0 [keV] 145400.0 145399:7� 0:4 145399:2� 0:4�2=� 613=540 770=540


052003-15

�2 ¼ Xi¼1;2

ðwi�stat;iÞ2 þXi¼1;2

ðwi�sys;iÞ2

þ 2w1w2X

j¼1;11

j�

K�sys;j�

K��sys;j : (13)

The statistical contribution is the first term and is simplycalculated using the individual measurements and theweights. The remaining two terms represent the systematicuncertainty, which is simply the remainder of the totaluncertainty after the statistical contribution has beensubtracted. The weighted results are � ¼ ð83:3� 1:2�1:4Þ keV and �m0 ¼ ð145425:9� 0:4� 1:7Þ keV.

VIII. SUMMARYAND CONCLUSIONS

We have measured the pole mass and the width of theD�þ meson with unprecedented precision, analyzing ahigh-purity sample of continuum-produced D�þ in eþe�collisions at approximately 10.6 GeV, equivalent to ap-proximately 477 fb�1, collected by the BABAR detector.The results for the two independent D0 decay modes agreewith each other well. The dominant systematic uncertaintyon the RBW pole position comes from the azimuthalvariation. For the decay modeD0 ! K��þ we obtain � ¼ð83:4� 1:7� 1:5Þ keV and �m0 ¼ ð145425:6� 0:6�1:7Þ keV while for the decay mode D0 ! K��þ��þwe obtain � ¼ ð83:2� 1:5� 2:6Þ keV and �m0 ¼ð145426:6� 0:5� 1:9Þ keV. Accounting for correlations,we obtain the combined measurement values � ¼ ð83:3�1:2� 1:4Þ keV and �m0 ¼ ð145425:9� 0:4� 1:7Þ keV.

The experimental value of gD�D� is calculated usingthe relationship between the width and the couplingconstant,

� ¼ �ðD0�þÞ þ �ðDþ�0Þ þ �ðDþ�Þ (14)

� �ðD0�þÞ þ �ðDþ�0Þ (15)

� g2D�D0�þ

24�m2D�þ

p3�þ þ

g2D�Dþ�0

24�m2D�þ

p3�0; (16)

where we have again ignored the electromagnetic contri-bution. The strong couplings can be related through

isospin by gD�D0�þ ¼ �ffiffiffi2

pgD�Dþ�0 [8]. Using � and the

mass values from Ref. [18] we determine the experimentalcoupling g

exp

D�D0�þ ¼ 16:92� 0:13� 0:14. The universalcoupling is directly related to the strong coupling by ĝ ¼gD�D0�þf�=ð2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimDmD�p Þ. This parametrization is differentfrom that of Ref. [8] and is chosen to match a commonchoice when using chiral perturbation theory, as inRefs. [4,21]. With this relation and f� ¼ 130:41 MeV,we find ĝexp ¼ 0:570� 0:004� 0:005.

The paper by Di Pierro and Eichten [22] quotes resultsin terms of a ratio, R ¼ �=ĝ2, which involves the widthof the particular state and provides a straightforwardmethod for calculating the corresponding value of the

universal coupling constant within their model. Thecoupling constant should then take the same value for

the selected Dð�Þ decay channels listed in Table V,which shows the values of the ratio R extracted fromthe model and the experimental values for �, as theywere in 2001. At the time of publication, ĝ was consis-tent for all of the modes in Ref. [22]. In 2010, BABARpublished much more precise results for the D1ð2420Þ0and D�2ð2460Þ0 [23]. Using those results, this measure-ment of �, and the ratios from Table V, we calculate newvalues for the coupling constant ĝ. Table VI shows theupdated results. We estimate the uncertainty on thecoupling constant value assuming �� . The updatedwidths reveal significant differences among the extractedvalues of ĝ.After completing this analysis, we became aware of

Rosner’s 1985 prediction that the D�þ natural linewidthshould be 83.9 keV [24]. He calculated this assuming asingle quark transition model to use P-wave K� ! K�decays to predict P-wave D� ! D� decay properties.Although he did not report an error estimate for thiscalculation in that work, his central value falls well withinour experimental precision. Using the same procedure andcurrent measurements, the prediction becomes ð80:5�0:1Þ keV [25]. A new lattice gauge calculation yielding�ðD�þÞ ¼ ð76� 7þ8�10Þ keV has also been reportedrecently [1].The order of magnitude increase in precision confirms

the observed inconsistency between the measured D�þwidth and the chiral quark model calculation by DiPierro and Eichten [22]. The precise measurements of thewidths presented in Table VI provide solid anchor pointsfor future calculations.

TABLE V. Selected rows from Table 11 of Ref. [22].State names correspond to the current PDG listings. The thirdcolumn is the ratio, R ¼ �=ĝ2, extracted from the model inRef. [22]. The values of ĝ were obtained from the data availablein 2001.

State Width (�) R (model) ĝ

D�ð2010Þþ 96� 4� 22 keV 143 keV 0:82� 0:09D1ð2420Þ0 18:9þ4:6�3:5 MeV 16 MeV 1:09þ0:12�0:11D�2ð2460Þ0 23� 5 MeV 38 MeV 0:77� 0:08

TABLE VI. Updated coupling constant values using the latestwidth measurements. Ratio values are taken from Table V.Significant differences are seen among the coupling constantscalculated using the updated width measurements.

State Width (�) R (model) ĝ

D�ð2010Þþ 83:3� 1:2� 1:4 keV 143 keV 0:76� 0:01D1ð2420Þ0 31:4� 0:5� 1:3 MeV 16 MeV 1:40� 0:03D�2ð2460Þ0 50:5� 0:6� 0:7 MeV 38 MeV 1:15� 0:01


052003-16

ACKNOWLEDGMENTS

We are grateful for the extraordinary contributionsof our PEP-II colleagues in achieving the excellentluminosity and machine conditions that have made thiswork possible. The success of this project also reliescritically on the expertise and dedication of the comput-ing organizations that support BABAR. The collaboratinginstitutions wish to thank SLAC for its support and thekind hospitality extended to them. This work is sup-ported by the U.S. Department of Energy and NationalScience Foundation, the Natural Sciences andEngineering Research Council (Canada), theCommissariat à l’Energie Atomique and InstitutNational de Physique Nucléaire et de Physique desParticules (France), the Bundesministerium für Bildungund Forschung and Deutsche Forschungsgemeinschaft(Germany), the Istituto Nazionale di Fisica Nucleare(Italy), the Foundation for Fundamental Research onMatter (The Netherlands), the Research Council ofNorway, the Ministry of Education and Science of theRussian Federation, Ministerio de Ciencia e Innovación(Spain), and the Science and Technology FacilitiesCouncil (United Kingdom). Individuals have receivedsupport from the Marie-Curie IEF program (EuropeanUnion) and the A. P. Sloan Foundation (U.S.A.). TheUniversity of Cincinnati is gratefully acknowledged forits support of this research through a WISE (Women inScience and Engineering) fellowship to C. Fabby.

APPENDIX

In this Appendix we present the covariance andcorrelation matrices for the fits described in Secs. VAand VB.

TABLEVIII.

Covariance

matrixfortheparam

etersfrom

thefitto

D0!

K��

þMCresolutionsample.Param

etersaredefined

inEqs.(4)and(5).Symmetricelem

entsare

suppressed. fNG

�q

f1

f2

�1

�2

�3

�1

�2

�3

fNG

3:263

10�8

�1:002

10�5

8:311

10�3

q�1

:139

10�4

�8:914

10�2

1:033

100

f1

�7:780

10�7

�3:250

10�4

3:662

10�3

1:581

10�4

f2

5:671

10�8

2:336

10�5

�2:627

10�4

�6:724

10�6

5:761

10�7

�1

1:064

1

0�1

3�2

:634

10�1

1�4

:741

10�1

01:426

10�1

0�3

:353

10�1

21:081

10�1

3

�2

�1:998

10�1

0�1

:059

10�7

9:350

10�7

2:265

10�8

�1:913

10�9

2:996

10�1

38:823

10�1

1

�3

�1:016

10�1

1�3

:919

10�9

4:775

10�8

1:158

10�9

�6:553

10�1

1�1

:423

10�1

3�1

:102

10�1

25:624

10�1

3

�1

�4:662

10�1

1�1

:949

10�8

2:196

10�7

1:012

10�8

�3:980

10�1

09:854

10�1

51:342

10�1

27:143

10�1

47:072

10�1

3

�2

�2:474

10�9

�1:035

10�6

1:173

10�5

1:584

10�7

�1:306

10�8

1:144

10�1

44:486

10�1

11:887

10�1

29:422

10�1

24:260

10�1

0

�3

�1:756

10�1

0�7

:341

10�8

8:275

10�7

2:942

10�8

�1:469

10�9

2:487

10�1

45:008

10�1

22:302

10�1

31:818

10�1

23:528

10�1

15:872

10�1

2

TABLE VII. Summary of the results from the fits to the MCresolution sample for the D0 ! K��þ and D0 ! K��þ��þchannels (statistical uncertainties only). Parameters are definedin Eqs. (4) and (5).

Parameter D0 ! K��þ D0 ! K��þ��þfNG 0:00559� 0:00018 0:0054� 0:00016� 1:327� 0:091 1:830� 0:092q �23:04� 1:02 �29:24� 1:07f1 0:640� 0:013 0:730� 0:008f2 0:01874� 0:00086 0:02090� 0:00069�1 (keV) 145402:36� 0:33 145402:84� 0:24�2 (keV) 145465:37� 9:39 145451:63� 7:83�3 (keV) 145404:58� 0:75 145399:07� 0:81�1 (keV) 119:84� 0:84 112:73� 0:52�2 (keV) 722:89� 20:6 695:04� 15:75�3 (keV) 212:31� 2:42 209:54� 2:41


052003-17

TABLE X. Covariance matrix for the parameters from the fit to D0 ! K��þ��þ MC resolution sample. Parameters are defined in Eqs. (4) and (5). Symmetric elements aresuppressed.

fNG � q f1 f2 �1 �2 �3 �1 �2 �3

fNG 2:746 10�8� 9:170 10�6 8:565 10�3q �1:076 10�4 �9:539 10�2 1:149 100f1 �3:981 10�7 �1:799 10�4 2:071 10�3 6:953 10�5f2 4:133 10�8 1:829 10�5 �2:100 10�4 �3:847 10�6 4:784 10�7�1 1:274 10�12 5:343 10�10 �6:776 10�9 �1:097 10�10 9:246 10�12 5:648 10�14�2 �1:434 10�10 �7:936e�08 6:757 10�7 1:332 10�8 �1:478 10�9 1:399 10�13 6:134 10�11�3 �1:909 10�13 2:382e�10 2:094 10�9 �6:916 10�10 1:981 10�11 �1:016 10�13 �1:394 10�12 6:582 10�13�1 �2:191 10�11 �9:918 10�9 1:142 10�7 4:099 10�9 �2:061 10�10 �5:895 10�15 7:264 10�13 �4:344 10�14 2:724 10�13�2 o� 1:669 10�9 �7:535e�07 8:781 10�6 7:332 10�8 �8:820 10�9 �2:122 10�13 2:902 10�11 �1:152 10�13 3:967 10�12 2:480 10�10�3 �1:428 10�10 �6:452 10�8 7:441 10�7 1:919 10�8 �1:303 10�9 �3:679 10�14 4:432 10�12 �1:616 10�13 1:084 10�12 2:561 10�11 5:806 10�12

TABLE IX. Parameter correlation coefficients for the parameters from the fit to D0 ! K��þ MC resolution sample. Parameters are defined in Eqs. (4) and (5). Symmetricelements are suppressed.

fNG � q f1 f2 �1 �2 �3 �1 �2 �3

fNG 1.000

� 0.608 1.000

q �0:621 �0:962 1.000f1 �0:343 �0:284 0.287 1.000f2 0.414 0.338 �0:340 �0:705 1.000�1 0.002 �0:001 �0:001 0.034 �0:013 1.000�2 �0:118 �0:124 0.098 0.192 �0:268 0.097 1.000�3 �0:075 �0:057 0.063 0.123 �0:115 �0:577 �0:156 1.000�1 �0:307 �0:254 0.257 0.958 �0:624 0.036 0.170 0.113 1.000�2 �0:664 �0:550 0.559 0.611 �0:834 0.002 0.231 0.122 0.543 1.000�3 �0:401 �0:332 0.336 0.966 �0:799 0.031 0.220 0.127 0.892 0.705 1.000

J.P.LEESet

al.

PHYSICALREVIEW

D88,052003(2013)

052003-18

TABLE XI. Parameter correlation coefficients for the parameters from the fit to D0 ! K��þ��þ MC resolution sample.Parameters are defined in Eqs. (4) and (5). Symmetric elements are suppressed.

fNG � q f1 f2 �1 �2 �3 �1 �2 �3

fNG 1.000� 0.598 1.000

q �0:606 �0:962 1.000f1 �0:288 �0:233 0.232 1.000f2 0.361 0.286 �0:283 �0:667 1.000�1 0.032 0.024 �0:027 �0:055 0.056 1.000�2 �0:110 �0:109 0.080 0.204 �0:273 0.075 1.000�3 �0:001 0.003 0.002 �0:102 0.035 �0:527 �0:219 1.000�1 �0:253 �0:205 0.204 0.942 �0:571 �0:048 0.178 �0:103 1.000�2 �0:639 �0:517 0.520 0.558 �0:810 �0:057 0.235 �0:009 0.483 1.000�3 �0:358 �0:289 0.288 0.955 �0:782 �0:064 0.235 �0:083 0.862 0.675 1.000

TABLE XII. Covariance matrix for the parameters from the fit to D0 ! K��þ data. Parameters are defined in Eqs. (7) and (8).Symmetric elements are suppressed.

�m0 Nsig Nbkg c �

�m0 3:181 10�13

4:060 10�10 4:909 10�5Nsig 3:782 10�6 3:533 10�1 1:199 104Nbkg �3:692 10�6 �3:448 10�1 �8:631 103 1:470 105c �6:288 10�9 �5:534 10�4 �1:711 101 1:668 101 7:936 10�2� �1:017 10�13 �9:965 10�9 �1:084 10�4 1:058 10�4 1:779 10�7 2:920 10�12

TABLE XIV. Covariance matrix for the parameters from the fit to D0 ! K��þ��þ data. Parameters are defined in Eqs. (7) and (8).Note that � and �m0 are measured in keV. Symmetric elements are suppressed.

�m0 Nbkg Nsig c �

�m0 2:206 10�13

2:586 10�10 4:605 10�5Nbkg 3:251 10�6 4:233 10�1 2:259 104Nsig �3:208 10�6 �4:179 10�1 �1:313 104 1:874 105c �1:742 10�9 �2:021 10�4 �8:226 100 8:095 100 1:678 10�2� �6:213 10�14 �8:633 10�9 �1:191 10�4 1:175 10�4 6:072 10�8 2:289 10�12

TABLE XIII. Parameter correlation coefficients for the parameters from the fit to D0 ! K��þ data. Parameters are defined inEqs. (7) and (8). Symmetric elements are suppressed.

�m0 Nsig Nbkg c �

�m0 1.000

0.103 1.000Nsig 0.061 0.461 1.000Nbkg �0:017 �0:128 �0:206 1.000c �0:040 �0:280 �0:555 0.154 1.000� �0:106 �0:832 �0:579 0.161 0.370 1.000


052003-19

[1] D. Becirevic and F. Sanfilippo, Phys. Lett. B 721, 94(2013).

[2] P. Singer, Acta Phys. Pol. B 30, 3849 (1999).[3] D. Guetta and P. Singer, Nucl. Phys. B, Proc. Suppl. 93,

134 (2001).[4] B. El-Bennich, M.A. Ivanov, and C.D. Roberts, Phys.

Rev. C 83, 025205 (2011).[5] G. Burdman, Z. Ligeti, M. Neubert, and Y. Nir, Phys. Rev.

D 49, 2331 (1994).[6] C. Arnesen, B. Grinstein, I. Rothstein, and I. Stewart,

Phys. Rev. Lett. 95, 071802 (2005).[7] J. Bailey et al., Phys. Rev. D 79, 054507 (2009).[8] A. Anastassov et al. (CLEO Collaboration), Phys. Rev. D

65, 032003 (2002).[9] J.M. Blatt and V. F. Weisskopf, Theoretical Nuclear

Physics (John Wiley & Sons, New York, 1952).[10] F. von Hippel and C. Quigg, Phys. Rev. D 5, 624

(1972).[11] H. Albrecht et al. (ARGUS Collaboration), Phys. Lett. B

308, 435 (1993).[12] A. J. Schwartz et al. (E791 Collaboration), in the 5th

International Conference on Quark Confinement and theHadron Spectrum, Gargnano, Italy, 2002 (arXiv:hep-ex/0212057).

[13] J. P. Lees et al. (BABAR Collaboration), Nucl. Instrum.Methods Phys. Res., Sect. A 726, 203 (2013).

[14] B. Aubert et al. (BABAR Collaboration), Nucl. Instrum.Methods Phys. Res., Sect. A 479, 1 (2002).

[15] B. Aubert et al. (BABAR Collaboration), arXiv:1305.3560[Nucl. Instrum. Methods Phys. Res., Sect. A (to bepublished)].

[16] R. Feynman, Photon-Hadron Interactions (W. A.Benjamin, Reading, 1972).

[17] B. Aubert et al. (BABAR Collaboration), Phys. Rev. D 72,052006 (2005).

[18] J. Beringer et al. (Particle Data Group), Phys. Rev. D 86,010001 (2012).

[19] S. Agostinelli et al. (GEANT4 Collaboration), Nucl.Instrum. Methods Phys. Res., Sect. A 506, 250(2003).

[20] E. Barberio and Z. Was, Comput. Phys. Commun. 79, 291(1994).

[21] A. Abada, D. Bećirević, Ph. Boucaud, G. Herdoiza, J.Leroy, A. Le Yaouanc, O. Pène, and J. Rodrı́guez-Quintero, Phys. Rev. D 66, 074504 (2002).

[22] M. Di Pierro and E. Eichten, Phys. Rev. D 64, 114004(2001).

[23] P. del Amo Sanchez et al. (BABAR Collaboration), Phys.Rev. D 82, 111101(R) (2010).

[24] J. L. Rosner, Comments Nucl. Part. Phys. 16, 109(1986).

[25] J. L. Rosner (private communication); arXiv:1307.2550.

TABLE XV. Parameter correlation coefficients for the parameters from the fit to D0 !K��þ��þ data. Parameters are defined in Eqs. (7) and (8). Note that � and �m0 aremeasured in keV. Symmetric elements are suppressed.

�m0 Nbkg Nsig c �

�m0 1.000

0.081 1.000Nbkg 0.046 0.415 1.000Nsig �0:016 �0:142 �0:202 1.000c �0:029 �0:230 �0:422 0.144 1.000� �0:087 �0:841 �0:524 0.179 0.310 1.000


052003-20
http://dx.doi.org/10.1016/j.physletb.2013.03.004http://dx.doi.org/10.1016/j.physletb.2013.03.004http://dx.doi.org/10.1016/S0920-5632(00)01077-Xhttp://dx.doi.org/10.1016/S0920-5632(00)01077-Xhttp://dx.doi.org/10.1103/PhysRevC.83.025205http://dx.doi.org/10.1103/PhysRevC.83.025205http://dx.doi.org/10.1103/PhysRevD.49.2331http://dx.doi.org/10.1103/PhysRevD.49.2331http://dx.doi.org/10.1103/PhysRevLett.95.071802http://dx.doi.org/10.1103/PhysRevD.79.054507http://dx.doi.org/10.1103/PhysRevD.65.032003http://dx.doi.org/10.1103/PhysRevD.65.032003http://dx.doi.org/10.1103/PhysRevD.5.624http://dx.doi.org/10.1103/PhysRevD.5.624http://dx.doi.org/10.1016/0370-2693(93)91309-Bhttp://dx.doi.org/10.1016/0370-2693(93)91309-Bhttp://arXiv.org/abs/hep-ex/0212057http://arXiv.org/abs/hep-ex/0212057http://dx.doi.org/10.1016/j.nima.2013.04.029http://dx.doi.org/10.1016/j.nima.2013.04.029http://dx.doi.org/10.1016/S0168-9002(01)02012-5http://dx.doi.org/10.1016/S0168-9002(01)02012-5http://arXiv.org/abs/1305.3560http://dx.doi.org/10.1103/PhysRevD.72.052006http://dx.doi.org/10.1103/PhysRevD.72.052006http://dx.doi.org/10.1103/PhysRevD.86.010001http://dx.doi.org/10.1103/PhysRevD.86.010001http://dx.doi.org/10.1016/S0168-9002(03)01368-8http://dx.doi.org/10.1016/S0168-9002(03)01368-8http://dx.doi.org/10.1016/S0168-9002(03)01368-8http://dx.doi.org/10.1016/0010-4655(94)90074-4http://dx.doi.org/10.1016/0010-4655(94)90074-4http://dx.doi.org/10.1103/PhysRevD.66.074504http://dx.doi.org/10.1103/PhysRevD.64.114004http://dx.doi.org/10.1103/PhysRevD.64.114004http://dx.doi.org/10.1103/PhysRevD.82.111101http://dx.doi.org/10.1103/PhysRevD.82.111101http://arXiv.org/abs/1307.2550

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